They pretty much stay in thier hole all the time. They are quite easy to keep once you get a healthy specimen. I have found that the key to keeping them happy is to have a decent sand bed (about 2" works or more) and provide them with plenty of rubble to build and line the walls of their cave. A hole in a pure sand bed does not work as it keeps collapsing and frustrates the fish into moving and jumping out of the tank.
Once it starts building a hole where you want it, start giving it some rubble rock near the hole and it will use them. Very fascinating to watch.
Heres mine. Tank set up in April. Jawfish introduced 5/21. They have stayed together like this until two days ago. They separated for a day, were back together for a day and are separated again.